Ex_1Dmotion

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General 1-D motion Average velocity: 2 1 2 1 ave x x x t t t υ Δ = = Δ Average acceleration: 2 1 2 1 ave a t t t υ υ υ Δ = = Δ Instantaneous velocity: dx dt υ = Instantaneous acceleration: 2 2 d d a dt dt υ = = x 0 Example 1. Particles A and B are moving along a straight line. Their positions are defined as m and m for s. 3 2 1.5 10 20 40 A x t t t = − + + 4 3 2 (1/6) (8/3) 5 15 10 B x t t t t = + + 0 1 t (a) At what time instant do these two particles have the same acceleration? Ans : t = 6 s (b) Calculate the average acceleration of A during the interval between t = 2 s and t = 6 s. Ans : 16 m/s 2 2. The position of a particle moving along a straight line is given by m for the duration of s. 3 2 ( ) 6 15 40 x t t t t = + 0 8 t (a) Draw the , , and x t t a t
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